MOLECULAR-TRANSPORT IN A 2-DIMENSIONAL LATTICE OF SORPTION SITES

It is known from experimental study of the sorption of some aromatic compounds (such as p-xylene) in zeolites with the MFI lattice that the adsorption kinetics in such systems exhibits appreciable deviations from the 2nd Fick law. To account for those deviations, whose origin lies in the crystal bulk, the existence of two phases which are not in local chemical equilibrium is postulated: a mobile phase is assumed to occur in the straight zeolite channels whereas an immobile phase is assumed in the zig-zag channels. A microkinetic model is proposed assuming localization of the sorbed molecules on two kinds of centres arranged in a regular two-dimensional lattice, along which migration takes place in agreement with the Langmuir kinetics of exchange of molecules between the occupied and unoccupied centres. For an exact description of the time evolution of the considered physical system the model results in a set of ordinary differential equations which are transformed into a system of two partial differential equations providing a spatially continuous description of the physical system. This approach enables the phenomenological kinetic parameters to be interpreted in terms of the jump frequency of molecules between the various kinds of adsorption centres. For small perturbations in the concentration of the sorbing substance the mathematical model is linearized, and the behaviour of the system is illustrated using the numerical solution of the model equations. In dependence on changes in the model parameters, the transition from the case of pure diffusion along a one-dimensional lattice in the mobile phase, with the zig-zag channels inaccessible, via the case of a slowly establishing local equilibrium between the two sub-lattices, to the limiting case of instantaneously establishing local equilibrium between the sub-lattices is discussed.